For what value of x are the points A(–3, 12), B(7, 6) and C(x, 9) collinear?
To show that the points are collinear, we show that the area of triangle is equilateral = 0
Δ = 0
Δ = 1/2{x1(y2−y3) + x2(y3−y1) + x3(y1−y2)}
⇒ Δ = 1/2{–3(6–9) + 7 (9 – 12) + x(12– 6)} = 0
⇒ (–3)(–3) + 7(–3) + 6x = 0
⇒ 9–21 + 6x = 0
6x = 12
x = 2